Mirror modifier creates duplicate vertices when modeling
Check the box of the 'bisect' Y axis in the mirror modifier.
The mirror modifier duplicates your whole mesh and mirrors it as a whole, so that's why there are duplicate vertices. To make it mirror only one side and get rid of the other, you must check the 'bisect' axis as well (bisecting literaly means cutting in half).
If the side it got rid of was not the one you wished to get rid, also check the 'flip' box in the same axis.